Methods (notes)

Due to skewed distributions, median values are reported with upper and lower limits of central 90% of observations. Unless otherwise noted, the realtionship between biomass gain (stem or area basis) and biomass quantity was modeled as an exponential negative relationship to log-DBH (\(growth = e^{a+b \times \log{DBH}}\)).

Urban forest structure in Boston

Tree canopy covered 32% of the study area of which 81% was within 10 m of an edge, but canopy, biomass, and fragmentation degree were distributed differently between LULC types (Figure 1). Developed and High-density Residential areas covering, respectively, 38% and 39% of the total urban area contained 16% and 49% of total canopy area of which 95% and 95% was within 10 m of an edge (Table S1 – canopy and biomass configuration summary). In contrast, while Forest areas covered only 8% of the study area they contained 23% of the total urban canopy and 32% of total biomass, of which only 36% was within 10 m of an edge. The extensive area of HD Residential land, containing a significant fraction of the total city biomass under highly fragmented conditions, implies a potentially large contribution of these types of canopy configurations to overall urban “forest” productivity, but which also requires specific accounting for urban- and canopy-specific influence on growth rates. In contrast, Forest-type land cover covered a small fraction of total land surface but contained a significant fraction of overall biomass and at much lower canopy fragmentation than other developed cover types. These relatively small areas of forest might as a result be expected to perform a significant proportion of total C uptake for the city, but under different growing conditions and uptake rates than in surrounding urban trees.

Growth rates in urban context

On an individual stem basis, urban trees grew more quickly and showed increased growth nearer to canopy edges (Figure 2). Rural forest trees grew more slowly than urban forest trees, with median DBH 22.4 (13.5-46.5) cm corresponding to median annual growth of 0.02 (0-0.077) kg/kg. The best fit model for rural stem growth rate (Table S2 – model coefficients and p values) (residual std. error 0.029) showed a significant negative relationship with log-DBH (p<0.001) and a significantly higher per-stem rate of growth in softwood species compared to hardwoods (p<0.001). On an areal basis, complete DBH measurements over 4.8 years in all rural forest trees >12 cm DBH showed a comparble significant negative exponential relationship (residual standard error (RSE) 0.01) between annual hardwood biomass gain (MgC per MgC/ha) and total biomass density (MgC/ha) (p<0.001), excluding plots with <25% hardwoods by total biomass (Figure S1 – plot level growth). Median areal growth rate in hardwood species in rural forest plots was 0.023 (0.01-0.058) MgC per MgC/ha, corresponding to median biomass denstiy of 90.9 (47.5-210.8) MgC/ha.

Trees in urban forest grew faster than in rural forest, and grew more quickly within 10 m of a canopy edge than in canopy interior (20-30 m). Median DBH of edge (<10 m) and interior stems was 18.2 cm and 18.9 cm, respectively, corresponding to median annual growth of 0.045 kg/kg and 0.03 kg/kg. The best fit model for urban forest stem growth rate (estimating random slopes and intercepts for sample plot, year interval, and stem ID) showed a significant negative relationship with log-DBH (p<0.005) and a significantly lower growth rate in interior-grown stems (p<0.027). Projecting these stem growth rates to the record of all stems >5 cm DBH by edge distance class in the urban forest plots, there was a corresponding significant linear relationship (RSE 0.004) an an areal basis between annual biomass gain and biomass density (p<0.001), with significant lower biomass gain overall in interior plots (p< 0.001). In the urban forest plots median areal growth rate in edge biomass was 0.032 (0.017-0.045) MgC per MgC/ha, corresponding to median edge biomass denstiy of 103.7 (89.3-279.6) MgC/ha. In contrast, in interior biomass median areal growth rate was 0.022 (0.018-0.027) MgC per MgC/ha, corresponding to median interior biomass denstiy of 87.5 (57.2-163.5) MgC/ha.

Stem growth rate was fastest in street trees, with median annual growth rate of 0.079 kg/kg corresponding to median DBH of 25.9. As in the other tree stem samples, the best fit model for street tree stem growth (RSE 0.362) showed a significant negative relationship with log-DBH (p<0.001). The sampling design of the street tree survey did not allow for these growth rates to be estimated on an areal basis as in the rural- and urban-forest samples, necessitating the simulation of indvidual stem assemblages to approximate biomass and productivity by cell across the study area. Is it worth presenting some aggregate stats on the simulated street tree results here?

Context How things compare to other measured rates in literature etc. The range and median stem DBH in each sample context were similar, but the street tree sample included very few conifers and a relatively large fraction of non-native taxa, primarily deciduous hardwoods including members of Gleditsia, Zelkova and Pyrus.

Estimates of biomass gain

Estimated biomass gain (MgC/yr) in the combined urban forest + street tree (Hybrid) model was 12942 MgC, with the largest annual biomass gains accruing in the Forest and HD Residential land use types (Table 1). In contrast, estimates of biomass growth rates made only on the basis of urban forest growth rates (including edge effects) predicted somewhat lower total biomass gain of 1.069610^{4} MgC. The Hybrid model showed greater biomass accural primarily to non-forested land use types like High-Density Residential, partly a result of accounting for biomass growth in these open-canopy areas by applying higher street tree-like growth factors. An estimation approach that applied rural forest growth factors to per-ha-canopy biomass density showed lower biomass gain in all land use categories (total gain of 7760) MgC, with a greater relative fraction of total biomass gain accruing to forest stands. This reduced estimate, particuarly in non-forested cover types, is partly the result of lower per-stem and per-area biomass gain in rural forest context than seen in urban forest or street trees. The Hybrid estimate apportioned biomass gains similarly to the distribution of total biomass across the study area, with most biomass gains occuring in the more common moderate-density pixels dominated by the open-canopy High-Density Residential type with higher street tree-like growth factors (Figure 3). The rural forest model, in contrast, applied lower rural forest-like growth factors overall and apportioned somewhat more total biomass gain into the less common high-density pixels dominated by Forest land cover type.

Effect of biomass density basis

The model results also illustrate the sensitivity of estimating biomass productivity to the method used to judge biomass density in heterogeneous scattered urban tree stands. An example of typical discontinous urban canopy in the study area shows that at moderate levels of both canopy and impervious cover, estimates of biomass density in a given area can vary from XXX MgC/ha-ground to XXX MgC/ha-canopy to XXX MgC/ha-pervious, and common remotely sensed measures of vegetation cover and function such as NDVI may indicate a relatively barren condition (Figure 4). The method of determining the areal basis (ground, canopy, or pervious area) for biomass density across the study area had significant and differential effects on biomass density distributions that varied with land use type (Figure S2). As this study used the empirical relationship between stand biomass density and productivity on an areal basis to estimate biomass gain from measured density in the study area, different estimates of biomass density can be expected to result in different estimates of biomass gain. For instance, in comparison to the results obtained via per-canopy-area biomass density estimates, applying rural forest growth factors to biomass density on a per-ground-area basis rendered an estimate of 1.069610^{4}, reasonably similar to the estimate obtained using edge-specific urban forest growth factors. These coinciding results, rather than reflecting similar underlying ecosystem processes, are instead likely an artifact of shifting the distribution of biomass density, when judged on this per-ground-area basis, generally lower due to the prevalence of discontinuous tree stands in the study area.

Conclusions

Estimating forest productivity in urban areas has often required reliance on incomplete or infrequent field survey of living trees, reliance on estimate approaches developed in other bioclimatic regions, or application of coarse-resolution remote sensing measurements that obscure heterogeneity in urban vegetation cover with meaningful ecosystem functional consequences, such as the prevalence of canopy edges. Difficulties in accurately estimating forest productivity in urban context may also be due to two general types of ambiguity: The fundamental relationship between tree size and productivity measured in rural forest stands may not be reflected in urban-grown trees that experience different canopy environments, nutrient inputs, and a host of other anthropogenic effects not present in rural forests. To address this ambituity, this work has attempted to apply size-to-growth-rate relationships that were measured in local urban-grown trees that may more accurately represent forest ecosystem processes at work in the local urban context.

The second ambiguity in estimating urban forest productivity is in the application of biomass density-to-productivity relationships to discontinous and heterogenous collections of urban trees that may apply clearly only to less intensively managed and impacted stands of continuous canopy trees at predictable stages of succession. Such approaches are often used to inventory C sequestration and annual uptake in rural forests, based on the predictable relationship between stand age (density) and C uptake (e.g. FIA COLE). In this work, biomass density in a functional sense was was estimated on the basis of high-resolution canopy coverage measured for each pixel. This constraint of canopy coverage in determining biomass density, while imperfect, arguably provides a better appraisal of the distribution of tree size (and by proxy growth rate) in a given area and a better basis for comparison to density-to-productivity estimates developed through measurements in continuous canopy forests. The extent of available pervious cover, we argue, is a less useful correction for functional biomass density because the size and stem density of urban trees is less constrained by the availabilty of open soil compared to the availability of open space for canopy. The presence in the Boston study area of implausibly high estimates of biomass density on a pervious basis (up to 5000 MgC/ha-pervious) is likely an artifact of the capacity of relatively large trees to grow in nearly completely paved conditions so long as adequate open space above the impervious surfaces is available for canopy exposure. The distribution of estimates of biomass density on a canopy basis, however, shows more realistic values, and may well more accurately indicate the relative sizes of trees present. On a canopy basis, biomass density distribution was somewhat higher in Forest type pixels dominated by larger mature trees, while developed pixel types show a wider lower range of densities, possibly reflecting a wider mix of generally younger street and backyard trees.

Without accounting for canopy coverage and spacing, the commonplace urban example of stands of discontinuous canopy with relatively mature large trees appears similar in density to younger lower-biomass stands of smaller trees spread evenly over the same area. Such stands in continuous forest context tend to grow relatively more quickly than more mature stands, and in the case of the Boston study area the relatively high frequency of discontinous stands with low- to moderate biomass density on a per-ground-area basis raised the overall estimate of total biomass gain. This example shows that uncritically mapping the growth to density relationship of continuous forests on onto discontinous urban tree stands lead to applying higher growth factors than are likely accurate. Thus even if accurate and reasonably spatially resolved inventories of forest carbon by area were available for a city, the potential differences in urban per-stem growth rate and the inability to adequately quantify “density” in an ecosystem functional sense would still produce difficulties in producing accurate estimates of C uptake.

Therefore you should be careful and do it the way we did it. Canopy is the better metric because…

As growth and C uptake in forest stands is very often predicted on the basis of biomass density (also a proxy for stand age), these ambiguities in the call for caution in selecting an appropriate method for ascertiaining biomass density, particularly in scattered open-canopy urban stands.